{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 26,
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 读取数据\n",
    "train = np.loadtxt('click.csv', delimiter=',', skiprows=1)\n",
    "train_x = train[:,0]\n",
    "train_y = train[:,1]\n",
    "\n",
    "plt.plot(train_x, train_y, 'o')\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "训练数据：\n",
      "[[ 1.          1.39433428  1.94416809]\n",
      " [ 1.          1.11069026  1.23363286]\n",
      " [ 1.          0.09554325  0.00912851]\n",
      " [ 1.         -1.59139223  2.53252924]\n",
      " [ 1.         -0.8449606   0.71395842]\n",
      " [ 1.          0.93154667  0.8677792 ]\n",
      " [ 1.         -1.38239138  1.91100592]\n",
      " [ 1.         -1.74067856  3.02996185]\n",
      " [ 1.          0.46875906  0.21973506]\n",
      " [ 1.          0.73747445  0.54386856]\n",
      " [ 1.         -0.11345761  0.01287263]\n",
      " [ 1.         -0.63595975  0.4044448 ]\n",
      " [ 1.         -0.36724436  0.13486842]\n",
      " [ 1.         -0.44188752  0.19526458]\n",
      " [ 1.          0.3045441   0.09274711]\n",
      " [ 1.          1.94669369  3.78961632]\n",
      " [ 1.          0.25975821  0.06747433]\n",
      " [ 1.          0.25975821  0.06747433]\n",
      " [ 1.         -1.23310505  1.52054807]\n",
      " [ 1.          0.84197488  0.70892169]]\n",
      "theta =  [0.968474   0.54917288 0.20861627]\n"
     ]
    }
   ],
   "source": [
    "# 数据标准化\n",
    "mu = train_x.mean()\n",
    "sigma = train_x.std()\n",
    "def standardize(x):\n",
    "    return (x - mu) / sigma\n",
    "train_x_std = standardize(train_x)\n",
    "\n",
    "# 训练数据矩阵\n",
    "def to_matrix(x):\n",
    "    return np.vstack([np.ones(x.size), x, x**2]).T\n",
    "X = to_matrix(train_x_std)\n",
    "print(\"训练数据：\")\n",
    "print(X)\n",
    "\n",
    "# 回归函数\n",
    "theta = np.random.rand(3)\n",
    "def f(x):\n",
    "    return np.dot(x, theta)\n",
    "\n",
    "print(\"theta = \", theta)\n",
    "\n",
    "# 误差函数\n",
    "def E(x, y):\n",
    "    return 0.5 * np.sum((f(x) - y) ** 2)\n",
    "\n",
    "# 均方误差\n",
    "def MSE(x, y):\n",
    "    return (1 / x.shape[0]) * np.sum((y - f(x)) ** 2)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第1次, theta = [9.5279322  2.40805417 9.17659083], 差值 = 153113.0506\n",
      "第2次, theta = [17.73684174  4.24219804 17.58523373], 差值 = 137848.6695\n",
      "第3次, theta = [25.61340023  6.05132336 25.46589087], 差值 = 124190.1568\n",
      "第4次, theta = [33.17481441  7.83519807 32.84817811], 差值 = 111966.4422\n",
      "第5次, theta = [40.43735455  9.59363586 39.76007653], 差值 = 101024.7400\n",
      "第6次, theta = [47.41640593 11.32649296 46.22802245], 差值 = 91228.5927\n",
      "第7次, theta = [54.12651737 13.03366514 52.2769925 ], 差值 = 82456.1240\n",
      "第8次, theta = [60.58144717 14.71508489 57.930584  ], 差值 = 74598.4791\n",
      "第9次, theta = [66.79420654 16.3707188  63.21109091], 差值 = 67558.4316\n",
      "第10次, theta = [72.7771006  18.00056506 68.13957558], 差值 = 61249.1394\n",
      "第11次, theta = [78.54176707 19.6046511  72.73593664], 差值 = 55593.0342\n",
      "第12次, theta = [84.099213   21.18303141 77.01897303], 差值 = 50520.8294\n",
      "第13次, theta = [89.45984928 22.73578546 81.00644458], 差值 = 45970.6343\n",
      "第14次, theta = [94.6335234  24.26301578 84.71512925], 差值 = 41887.1635\n",
      "第15次, theta = [99.62955035 25.76484612 88.16087719], 差值 = 38221.0301\n",
      "第16次, theta = [104.4567418   27.24141972  91.35866188], 差值 = 34928.1150\n",
      "第17次, theta = [109.12343372  28.69289776  94.32262837], 差值 = 31969.0041\n",
      "第18次, theta = [113.63751248  30.11945781  97.06613895], 差值 = 29308.4850\n",
      "第19次, theta = [118.00643945  31.5212924   99.60181624], 差值 = 26915.0976\n",
      "第20次, theta = [122.23727434  32.89860774 101.94158396], 差值 = 24760.7336\n",
      "第21次, theta = [126.33669717  34.25162246 104.09670543], 差值 = 22820.2776\n",
      "第22次, theta = [130.31102912  35.58056643 106.07781993], 差值 = 21071.2880\n",
      "第23次, theta = [134.16625214  36.88567969 107.89497712], 差值 = 19493.7108\n",
      "第24次, theta = [137.90802755  38.16721141 109.55766949], 差值 = 18069.6245\n",
      "第25次, theta = [141.54171361  39.42541895 111.07486307], 差值 = 16783.0127\n",
      "第26次, theta = [145.07238208  40.66056696 112.45502646], 差值 = 15619.5603\n",
      "第27次, theta = [148.50483391  41.87292655 113.70615823], 差值 = 14566.4722\n",
      "第28次, theta = [151.84361407  43.0627745  114.8358128 ], 差值 = 13612.3105\n",
      "第29次, theta = [155.09302553  44.23039253 115.85112496], 差值 = 12746.8501\n",
      "第30次, theta = [158.25714252  45.37606661 116.75883298], 差值 = 11960.9491\n",
      "第31次, theta = [161.33982301  46.50008637 117.56530045], 差值 = 11246.4334\n",
      "第32次, theta = [164.34472054  47.60274446 118.27653695], 差值 = 10595.9931\n",
      "第33次, theta = [167.27529539  48.68433599 118.8982176 ], 差值 = 10003.0907\n",
      "第34次, theta = [170.13482513  49.74515808 119.43570143], 差值 = 9461.8789\n",
      "第35次, theta = [172.9264146   50.78550932 119.89404886], 差值 = 8967.1264\n",
      "第36次, theta = [175.65300533  51.80568934 120.27803815], 差值 = 8514.1532\n",
      "第37次, theta = [178.31738446  52.80599842 120.59218096], 差值 = 8098.7710\n",
      "第38次, theta = [180.92219315  53.7867371  120.84073708], 差值 = 7717.2315\n",
      "第39次, theta = [183.46993455  54.74820579 121.02772827], 差值 = 7366.1795\n",
      "第40次, theta = [185.96298129  55.6907045  121.15695145], 差值 = 7042.6106\n",
      "第41次, theta = [188.40358264  56.6145325  121.23199104], 差值 = 6743.8348\n",
      "第42次, theta = [190.79387116  57.51998802 121.25623077], 差值 = 6467.4421\n",
      "第43次, theta = [193.13586912  58.40736807 121.23286467], 差值 = 6211.2736\n",
      "第44次, theta = [195.43149445  59.27696809 121.16490759], 差值 = 5973.3945\n",
      "第45次, theta = [197.68256641  60.12908185 121.05520509], 差值 = 5752.0704\n",
      "第46次, theta = [199.89081098  60.96400116 120.90644275], 差值 = 5545.7459\n",
      "第47次, theta = [202.0578659   61.78201572 120.72115506], 差值 = 5353.0261\n",
      "第48次, theta = [204.18528548  62.58341296 120.50173371], 差值 = 5172.6591\n",
      "第49次, theta = [206.2745451   63.36847787 120.25043551], 差值 = 5003.5213\n",
      "第50次, theta = [208.32704549  64.1374929  119.96938983], 差值 = 4844.6037\n",
      "第51次, theta = [210.34411678  64.89073776 119.66060564], 差值 = 4694.9996\n",
      "第52次, theta = [212.32702233  65.62848938 119.32597817], 差值 = 4553.8944\n",
      "第53次, theta = [214.27696232  66.35102179 118.9672952 ], 差值 = 4420.5554\n",
      "第54次, theta = [216.19507717  67.05860598 118.58624299], 差值 = 4294.3233\n",
      "第55次, theta = [218.08245077  67.75150991 118.1844119 ], 差值 = 4174.6046\n",
      "第56次, theta = [219.94011352  68.42999834 117.76330169], 差值 = 4060.8649\n",
      "第57次, theta = [221.76904521  69.09433285 117.32432655], 差值 = 3952.6221\n",
      "第58次, theta = [223.57017778  69.74477173 116.86881981], 差值 = 3849.4418\n",
      "第59次, theta = [225.34439782  70.38156996 116.39803844], 差值 = 3750.9316\n",
      "第60次, theta = [227.0925491   71.00497916 115.91316725], 差值 = 3656.7370\n",
      "第61次, theta = [228.81543477  71.61524758 115.41532293], 差值 = 3566.5379\n",
      "第62次, theta = [230.51381962  72.21262003 114.90555777], 差值 = 3480.0441\n",
      "第63次, theta = [232.18843207  72.79733789 114.38486327], 差值 = 3396.9931\n",
      "第64次, theta = [233.83996616  73.3696391  113.85417351], 差值 = 3317.1468\n",
      "第65次, theta = [235.46908337  73.92975812 113.31436831], 差值 = 3240.2893\n",
      "第66次, theta = [237.07641434  74.47792595 112.76627624], 差值 = 3166.2242\n",
      "第67次, theta = [238.66256053  75.01437012 112.2106775 ], 差值 = 3094.7729\n",
      "第68次, theta = [240.22809576  75.5393147  111.64830659], 差值 = 3025.7730\n",
      "第69次, theta = [241.77356772  76.05298027 111.07985481], 差值 = 2959.0761\n",
      "第70次, theta = [243.29949927  76.55558398 110.50597273], 差值 = 2894.5470\n",
      "第71次, theta = [244.80638983  77.04733954 109.92727239], 差值 = 2832.0619\n",
      "第72次, theta = [246.29471658  77.52845722 109.34432949], 差值 = 2771.5076\n",
      "第73次, theta = [247.76493566  77.99914391 108.7576854 ], 差值 = 2712.7803\n",
      "第74次, theta = [249.21748324  78.45960308 108.16784905], 差值 = 2655.7845\n",
      "第75次, theta = [250.65277659  78.91003485 107.57529877], 差值 = 2600.4327\n",
      "第76次, theta = [252.07121509  79.35063602 106.98048398], 差值 = 2546.6441\n",
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      "第82次, theta = [260.24822697  81.7984064  103.38595369], 差值 = 2252.9344\n",
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      "第88次, theta = [267.90242811  83.93826231  99.79658886], 差值 = 2000.7253\n",
      "第89次, theta = [269.13144777  84.26750844  99.20266273], 差值 = 1962.0950\n",
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      "第97次, theta = [278.52380516  86.64706623  94.52704989], 差值 = 1682.6596\n",
      "第98次, theta = [279.64578806  86.91482647  93.95403968], 差值 = 1651.0691\n",
      "第99次, theta = [280.7567915   87.17643664  93.38392642], 差值 = 1620.1505\n",
      "第100次, theta = [281.85697715  87.43202375  92.81679497], 差值 = 1589.8852\n",
      "第101次, theta = [282.9465017   87.68171241  92.25272341], 差值 = 1560.2556\n",
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      "第737次, theta = [405.52057682  95.11764138  23.4060728 ], 差值 = 0.0270\n",
      "第738次, theta = [405.52504382  95.11733239  23.40351084], 差值 = 0.0265\n",
      "第739次, theta = [405.52947273  95.11702603  23.40097074], 差值 = 0.0260\n",
      "第740次, theta = [405.53386386  95.11672227  23.3984523 ], 差值 = 0.0256\n",
      "第741次, theta = [405.53821754  95.11642109  23.39595535], 差值 = 0.0252\n",
      "第742次, theta = [405.54253408  95.11612247  23.39347969], 差值 = 0.0247\n",
      "第743次, theta = [405.5468138   95.11582639  23.39102515], 差值 = 0.0243\n",
      "第744次, theta = [405.55105703  95.11553282  23.38859154], 差值 = 0.0239\n",
      "第745次, theta = [405.55526405  95.11524176  23.38617869], 差值 = 0.0235\n",
      "第746次, theta = [405.5594352   95.11495316  23.38378642], 差值 = 0.0231\n",
      "第747次, theta = [405.56357077  95.11466702  23.38141455], 差值 = 0.0227\n",
      "第748次, theta = [405.56767106  95.11438331  23.37906292], 差值 = 0.0223\n",
      "第749次, theta = [405.57173638  95.11410202  23.37673134], 差值 = 0.0219\n",
      "第750次, theta = [405.57576703  95.11382311  23.37441965], 差值 = 0.0216\n",
      "第751次, theta = [405.57976329  95.11354658  23.37212767], 差值 = 0.0212\n",
      "第752次, theta = [405.58372547  95.1132724   23.36985525], 差值 = 0.0208\n",
      "第753次, theta = [405.58765386  95.11300055  23.3676022 ], 差值 = 0.0205\n",
      "第754次, theta = [405.59154874  95.11273101  23.36536838], 差值 = 0.0201\n",
      "第755次, theta = [405.5954104   95.11246376  23.3631536 ], 差值 = 0.0198\n",
      "第756次, theta = [405.59923912  95.11219879  23.36095772], 差值 = 0.0195\n",
      "第757次, theta = [405.60303518  95.11193607  23.35878057], 差值 = 0.0191\n",
      "第758次, theta = [405.60679886  95.11167558  23.35662198], 差值 = 0.0188\n",
      "第759次, theta = [405.61053045  95.11141731  23.35448181], 差值 = 0.0185\n",
      "第760次, theta = [405.6142302   95.11116124  23.35235989], 差值 = 0.0182\n",
      "第761次, theta = [405.6178984   95.11090734  23.35025607], 差值 = 0.0179\n",
      "第762次, theta = [405.62153531  95.1106556   23.3481702 ], 差值 = 0.0176\n",
      "第763次, theta = [405.6251412   95.11040601  23.34610211], 差值 = 0.0173\n",
      "第764次, theta = [405.62871633  95.11015854  23.34405166], 差值 = 0.0170\n",
      "第765次, theta = [405.63226097  95.10991317  23.34201871], 差值 = 0.0167\n",
      "第766次, theta = [405.63577538  95.10966989  23.34000309], 差值 = 0.0164\n",
      "第767次, theta = [405.63925981  95.10942868  23.33800467], 差值 = 0.0161\n",
      "第768次, theta = [405.64271452  95.10918952  23.33602328], 差值 = 0.0159\n",
      "第769次, theta = [405.64613977  95.1089524   23.3340588 ], 差值 = 0.0156\n",
      "第770次, theta = [405.64953579  95.10871729  23.33211108], 差值 = 0.0153\n",
      "第771次, theta = [405.65290286  95.10848418  23.33017997], 差值 = 0.0151\n",
      "第772次, theta = [405.6562412   95.10825306  23.32826533], 差值 = 0.0148\n",
      "第773次, theta = [405.65955107  95.1080239   23.32636702], 差值 = 0.0145\n",
      "第774次, theta = [405.66283271  95.1077967   23.3244849 ], 差值 = 0.0143\n",
      "第775次, theta = [405.66608636  95.10757142  23.32261883], 差值 = 0.0141\n",
      "第776次, theta = [405.66931225  95.10734807  23.32076868], 差值 = 0.0138\n",
      "第777次, theta = [405.67251063  95.10712661  23.31893431], 差值 = 0.0136\n",
      "第778次, theta = [405.67568173  95.10690704  23.31711559], 差值 = 0.0134\n",
      "第779次, theta = [405.67882579  95.10668934  23.31531238], 差值 = 0.0131\n",
      "第780次, theta = [405.68194303  95.10647349  23.31352455], 差值 = 0.0129\n",
      "第781次, theta = [405.68503367  95.10625948  23.31175196], 差值 = 0.0127\n",
      "第782次, theta = [405.68809796  95.10604728  23.3099945 ], 差值 = 0.0125\n",
      "第783次, theta = [405.69113611  95.1058369   23.30825203], 差值 = 0.0123\n",
      "第784次, theta = [405.69414835  95.1056283   23.30652442], 差值 = 0.0121\n",
      "第785次, theta = [405.69713489  95.10542148  23.30481154], 差值 = 0.0118\n",
      "第786次, theta = [405.70009596  95.10521642  23.30311327], 差值 = 0.0116\n",
      "第787次, theta = [405.70303178  95.10501311  23.30142949], 差值 = 0.0114\n",
      "第788次, theta = [405.70594255  95.10481153  23.29976007], 差值 = 0.0113\n",
      "第789次, theta = [405.7088285   95.10461166  23.29810489], 差值 = 0.0111\n",
      "第790次, theta = [405.71168983  95.10441349  23.29646383], 差值 = 0.0109\n",
      "第791次, theta = [405.71452676  95.10421701  23.29483676], 差值 = 0.0107\n",
      "第792次, theta = [405.71733949  95.10402221  23.29322357], 差值 = 0.0105\n",
      "第793次, theta = [405.72012823  95.10382906  23.29162414], 差值 = 0.0103\n",
      "第794次, theta = [405.72289318  95.10363755  23.29003836], 差值 = 0.0102\n",
      "第795次, theta = [405.72563455  95.10344768  23.2884661 ], 差值 = 0.0100\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 求theta\n",
    "diff = 1\n",
    "ETA = 1e-3\n",
    "error = E(X, train_y)\n",
    "errors = [MSE(X, train_y)]\n",
    "count  = 0\n",
    "\n",
    "while diff > 1e-2:\n",
    "    theta = theta - ETA * np.dot(f(X) - train_y, X)\n",
    "    error_current = E(X, train_y)\n",
    "    diff = error - error_current\n",
    "    error = error_current\n",
    "    errors.append(MSE(X, train_y))\n",
    "    count += 1\n",
    "    log = '第{}次, theta = {}, 差值 = {:.4f}'\n",
    "    print(log.format(count, theta, diff))\n",
    "\n",
    "axis_x = np.linspace(-3, 3, 100)\n",
    "plt.plot(train_x_std, train_y, 'o')\n",
    "plt.plot(axis_x, f(to_matrix(axis_x)))\n",
    "plt.show()\n",
    "\n",
    "axis_x2 = np.arange(len(errors))\n",
    "plt.plot(axis_x2, errors)\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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    "source": [
     "# 多项式回归\n",
     "# author: chan\n",
     "# date: 2023/1/28\n"
    ],
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